Question

using AP the first 10 term is 150 and sum of its next ten terms is 550 find the ap ​

Answer 1

Question: In an A.P sum of first ten terms is −150 and the sum of its next ten terms is −550, Find the A.P.

Answer:

The sum of the first n terms of an AP is

Sₙ = n/2[2a + (n-1)-d]

n = 10, S₁₀ = -150

-150 = (10/2)[2a + (10 - 1)d]

-150 = 5[2a + 9d]

Dividing through by 5,

-30 = 2a + 9d ----------(1)

Given sum of its next 10 terms is - 550

n = 10, Sn = - 550

Here, a = a + 10d

- 550 = (10/2)[2(a + 10d) + (10-1)d]

- 550 = 5[2a + 29d]

Dividing through by 10,

-110 = 2a + 29d ----------(2)

Solving (1) and (2) we get

d = -4 and a = 3

So, the AP is 3, -1, -5, -9, -13 and so-on

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